Microreactors are devices utilized to manipulate and/or react chemical reagents in small-scale, controllable volumes. Because such reagents (and/or their reaction products) are often caustic and/or corrosive, microreactors frequently feature networks of microchannels etched out of plates of corrosion-resistant material, for example as described in International Patent Application Publication No. WO2007/112945, the entire disclosure of which is incorporated by reference herein. While such systems frequently do include entire separate modules (e.g., separate plates) for conducting heat away from the reaction channels, the use of entire plates of the corrosion-resistant material (1) can be quite expensive, and (2) deleteriously impacts the efficiency of heat exchange, as the heat produced by the reactions in the microreactor must be conducted not only through the channels themselves but also through the remaining thickness of the plate and through the interface between the reaction module and the heat-exchange module before reaching a heat-exchange module. Thus, there is a need for microreactor designs that minimize the use of expensive, non-thermally-conductive corrosion-resistant materials in order to improve the conduction of heat out of the microreactor.